In the art of conventional gymnastic bikes, the motion of pedalling a bike occurs by holding a stationary handle with the hands and pedalling the pedals with the feet in circular motions, whereby parts of the user's legs are exercised. If desired, the handles may be pulled or pushed for providing stretching motions. However, conventional gymnastic bikes are equipped so as to have either a rotational motion around the stationary shaft or a stretching motion by use of the handles only, such that a simultaneous pedalling exercise for both the hands and feet is not allowed. In order to improve the functioning of conventional gymnastic bikes, the applicant disclosed in U.S. Pat. No. 4,842,269 and European Patent Application Serial No. 88311021.5 entitled "Multi-functional Stationary Bike for Gymnastic Purpose", a bike mounting that is equipped with an exercise mechanism for the handles and a motion mechanism for the foot pedals. In this fashion, the user is able to receive a full body exercise through laterally reciprocating circular motions that are produced by the hand-exercise mechanism, and longitudinally reciprocating circular motions that are produced by the foot-exercise mechanism. However, the hand-exercise and foot-exercise mechanisms are complicated being comprised of multiple members that are not convenient for assembly and disassembly thereof, and that are expensive to produce and process. This design shall be improved further, so as to enable the gymnastic bike to be more widely used.